# Math Help - Reflecting Telescope

1. ## Reflecting Telescope

A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 4 inches across at its opening and is 3 feet deep, where will the collected light be concentrated?

2. Originally Posted by magentarita
A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 4 inches across at its opening and is 3 feet deep (ähemm! are you sure?) , where will the collected light be concentrated?
I assume that the paraboloid has an opening of 4'' and a depth of 3''. If so:

The cross-section of the paraboloid through the focus and the vertex of the paraboloid must be a parabola. Use a coordinate system where the vertex is V(0, 0) and the point P(3, 2) are located on the parabola.

The general equation of a parabola opening to the right is:

$y^2 = 2p\cdot x$

Use the coordinates of P to calculate p. (I've got $p = \frac23$)

Then the focus F is the point where all parallel light rays will be concentrated. F has the coordinates $F\left(\frac p2\ ,\ 0\right)$

3. ## ok....

Originally Posted by earboth
I assume that the paraboloid has an opening of 4'' and a depth of 3''. If so:

The cross-section of the paraboloid through the focus and the vertex of the paraboloid must be a parabola. Use a coordinate system where the vertex is V(0, 0) and the point P(3, 2) are located on the parabola.

The general equation of a parabola opening to the right is:

$y^2 = 2p\cdot x$

Use the coordinates of P to calculate p. (I've got $p = \frac23$)

Then the focus F is the point where all parallel light rays will be concentrated. F has the coordinates $F\left(\frac p2\ ,\ 0\right)$